As you already know, your iPad has a feature called "Airplay Mirroring", which allows you to project the "mirror image" of whatever is on the screen onto a projector. So rather than having your iPad tethered to a cable that connects to the projector, why not have the freedom of moving around the room with your iPad in hand? A wireless connection, utilizing the iPad's ability to project the mirror image of what is on your device, giving you power, flexibility, and control.
The Apple TV is made for the iPad. It is the "Screen Mirroring" icon that you are looking. For iPads that run on iOS 12 or later, swipe down from the upper-right corner of the screen to bring up the AirPlay menu. You will see the image set forth below. Touch “Screen Mirroring.” For iPads that run on iOS 11 or earlier, swipe up from the bottom of the screen to bring up the AirPlay menu. Then touch “Screen Mirroring.”